The current invention relates to a method for designing an ophthalmic lens element, the method comprising the steps of determining a wavefront aberration of an eye to be minimized in a reference plane, wherein the wavefront aberration of the eye can be described by a first series of polynomials of ascending order up to a first specific order and corresponding first coefficients, and determining a first vision correction of a second specific order to obtain an adapted ophthalmic lens element.
Further, the current invention relates to a method for manufacturing an ophthalmic lens element comprising the steps of the method for designing an ophthalmic lens element.
Furthermore, the current invention is related to a computer program product for carrying out the steps of the aforementioned methods.
Ophthalmic lenses for vision correction are well-known in the state of the art for hundreds of years. They have been used by opticians, optometrists and ophthalmologists for correcting nearsightedness and farsightedness by using concave and convex lenses, respectively, as well as for correcting presbyopia using multifocal lenses.
Wavefront aberrations are the result of differences in optical path length between the ideal wavefront that would result in a perfect focus through an optical system, i.e. an eyeglass and the eye, and the aberrated wavefront that is produced by the actual optical system. Wavefront aberrations are often categories by their radial order, which indicates the dependence of the aberration on pupil size. The optical components of the human eye suffer from both “low-order” and “high-order” wavefront aberrations. The low-order aberrations of interest to the correction of vision are actually a subset of the low-order aberrations, referred to as the “second-order” wavefront aberrations. Second-order aberrations vary as a function of the square of the distance from the center of the pupil or aperture. These wavefront aberrations are typically corrected with an eyeglass prescription that includes a spherical power component, a cylindrical power component and an axis component that describes the orientation of the cylindrical power.
High-order aberrations represent wavefront aberrations but vary as a cubic function or higher of the distance from the center of the pupil or aperture. The high-order aberrations of the eye include aberrations such as, for example, coma, trefoil and spherical aberrations. Although these aberrations are often smaller in magnitude than the low-order aberrations, high-order aberrations of the eye can also degrade vision quality and limit visual performance. It is possible to improve vision quality by correcting the high-order aberrations of the eye in addition to the low-order aberrations. The eye examination procedure for traditional eyeglass prescriptions, however, only yields a correction that minimizes the low-order aberration of the eye. Correcting the high-order aberrations of the eye is not practical with ophthalmic lenses, because more significant low-order wavefront aberrations are introduced as the eye rotates behind the lens.
Moreover, ophthalmic lenses with refracted wavefront profiles that depart from a section of a perfect sphere or toric surface also produce various high-order wavefront aberrations. High-order aberrations may be produced under certain circumstances by the refraction of light through certain regions of lenses with spherical or toric surfaces, including symmetrical optical systems that suffer from classic Seidel spherical aberration or coma. Moreover, high-order aberrations may be routinely produced by the lens when at least one surface of the lens has non-zero third partial derivatives. This includes any lens with a surface that varies smoothly in curvature, including but not limited to single vision lenses, spherical lenses and progressive additional lenses. In particular, progressive additional lenses produce significant coma and trefoil within the progressive corridor and at the boundaries between the central viewing zones of the lens and the peripheral regions. Both low- and high-order aberrations are unavoidable in certain areas of progressive additional lenses due to the use of blending regions that provide a smooth change in addition power without visible lines of demarcation.
The wavefront aberrations produced by an ophthalmic lens interact with the wavefront aberrations of the eye. Aberration coupling occurs that can either improve or degrade vision quality through different regions of the lens, depending upon the low- and high-order aberrations present in the eye and through the ophthalmic lens. Traditionally, however, ophthalmic lenses have been designed to minimize only the magnitude of the low-order aberrations produced by both the eye and the ophthalmic lens. This is due to the inability heretofore of measuring the high-order wavefront aberrations of the eye, prior to the advent of commercially available wavefront sensors; the inability of correcting the high-order aberrations of the eye with an ophthalmic lens without introducing more significant low-order wavefront aberrations; and to the inability heretofore of machining ophthalmic lens surfaces of suitable complexity, prior to the advent of modern free-form surfacing techniques.
Although ophthalmic lenses cannot eliminate high-order wavefront aberrations without introducing additional aberrations, it is nevertheless possible to improve vision quality with ophthalmic lenses by minimizing the net effect upon vision of the combined optical interaction between the low- and high-order wavefront aberrations of the eye when determining the low-order eyeglass correction. Ophthalmic lenses are presently available with low-order eye glass corrections that have been manipulated to account for the effects of the high-order aberrations of the eye. For example, similar methods are disclosed in US patent application 2007/0279586 A1 and US patent application 2009/0015787 A1. These ophthalmic lenses provide the wearer with a “wavefront-optimized” vision correction that has had the spherical power component, cylindrical power component and cylindrical axis manipulated in order to improve vision quality based upon wavefront aberration measurements from a wavefront sensor.
Recently, ophthalmic lenses have also been introduced that seek to minimize the high-order aberrations produced by only the lens at least within the mathematical constraints of progressive addition surfaces, although this will not improve the maximum potential vision quality of the wearer. A similar method is, for example, disclosed in U.S. Pat. No. 7,063,421.
The high-order wavefront aberrations of the human eye vary significantly within the population. Further, the high-order wavefront aberrations across ophthalmic lenses with significant changes in power, such as progressive addition lenses, also vary significantly over the lens aperture. It is possible, however, to manipulate the optics of an ophthalmic lens for a given eyeglass wearer through a suitable mathematical optimization process prior to fabrication using a free-form production method which is, for example, suggested in U.S. Pat. No. 6,089,713. Further, it is possible to estimate vision quality by assessing wavefront aberrations. Therefore, it is possible to optimize the visual performance through different zones of an ophthalmic lens when the wavefront aberrations of the eye and the original ophthalmic lens design are both known.
The low-order refractive power of an ophthalmic lens element normally varies as a function of viewing angle both as a result of changes across one or more lens surfaces and as a result of astigmatism introduced by the oblique refraction of incident light. A typical optical design process seeks to preserve as closely as possible the intended low-order eyeglass correction for the wearer as the wearer gazes over the lens aperture at least within the inherent mathematical limitations of the lens design. In particular, progressive addition lens elements possess regions over the lens aperture in which it is not possible to provide the intended low-order eyeglass correction due to the presence of significant aberrations in blending regions of the surface.
Ophthalmic lens elements can produce high-order aberrations across the lens aperture as well, which may result from the refraction of light at wide field angles or from variations in curvature across one or more of the lens surfaces. For instance, because progressive lens elements rely on non-zero third derivatives in order to produce a smooth change in addition power over the lens aperture, the high-order aberrations of a progressive lens element vary as a function of the mixed partial derivatives of the progressive surface. Further, the high-order aberrations produced by a progressive lens are constrained primarily by the distribution of power and astigmatism over the lens surface, which represents a fundamental characteristic of the lens design. High-order aberrations referred to as “coma” (Z6 and Z9) and “trefoil” (Z7 and Z8) in the Zernike representation of high-order aberrations are directly influenced by the mixed partial derivatives of an ophthalmic lens surface described by a surface height function Z. The expansion of the Zernike polynomials can, for example, be derived from Gross et al., “Handbook of Optical Systems”, Vol. 1 to 6, WILEY-VCH Publishing, Weinheim, 2007, ISBN: 978-3-527-40382-0”.
In ophthalmic lens design, the intended or “target” distribution of low-order wavefront aberrations is typically specified. This distribution generally represents the ideal optical performance of the lens design for a particular combination of eyeglass prescription powers and fitting parameters. A typical optimization process seeks to achieve the desired distribution of optical powers as closely as possible by manipulating one or more continuously smooth surfaces of an ophthalmic lens element. At multiple points across the lens aperture, differences in optical performance between the modeled ophthalmic lens element and the target distribution are assessed using computer ray tracing for an assumed position of wear, which represents the position of the fitted lens on the wearer. During a typical ray tracing procedure, the refraction through the lens element of a quantity of rays from a specified object point, sufficient to characterize the wavefront aberrations of the lens up to the chosen order, are calculated. Ideally, these rays should all converge at the ideal focal plane of the eye associated with the object distance, although this is frequently not mathematically possible at all points across the lens aperture.
Typically, “merit functions” or least-square solutions representing the total magnitude of optical aberrations at these points are minimized at each of the specified points across the lens aperture using mathematical optimization and modeling techniques, such as finite element analysis. Further, these merit functions or the individual terms of these merit functions may also be weighted differently over the lens aperture in order to maximize visual performance in certain regions of the lens, wherein vision quality is most critical, or to minimize optimization in regions of the lens wherein certain optical aberrations are unavoidable due to the nature of the lens design. Common optimization techniques can also be derived from Gross et al. cited above.
In the current state of the art, these merit functions seek only to improve the performance of the ophthalmic lens element using a single, low-order (second-order) vision correction, or eyeglass prescription, originally specified by the eye care professional. Differences from this low-order single vision correction are therefore minimized over critical regions of the lens. Additional optimization terms may be incorporated in the merit function to minimize gradients of power (or astigmatism) or other optical attributes in order to reduce image swim or otherwise improve visual performance. Although it has been proven that the high-order aberrations of the eye cannot be corrected without introducing significant low-order aberrations of greater magnitude, visual performance can be improved by accounting for these aberrations when determining the traditional low-order vision correction or eyeglass prescription. Further, when an ophthalmic lens element introduces high-order aberrations that vary across the lens aperture, the ideal low-order vision correction also varies as a function of position over the lens.
Therefore, it is an object of the present invention to minimize the impact of the combined high-order aberrations produced by both the eye and the ophthalmic lens element over the lens aperture by accounting for the interaction between the high-order aberrations of the eye, as derived from measurements by an aberrometer or wavefront sensor, and the high-order aberrations of the ophthalmic lens element over the lens aperture.
It is a further object of the present invention to minimize the low-order wavefront aberrations of the ophthalmic lens element over specified regions of the lens aperture in addition to the low-order aberrations of the eye, traditionally eliminated by ophthalmic lens elements providing the desired spherical or sphero-cylindrical vision corrections.
Additionally, it is an object of the present invention to maximize vision quality over a range of viewing conditions, including ambient light levels or vary pupil sizes, by modifying the low-order vision correction to further improve vision quality in the presence of high-order wavefront aberrations within the eye and, more specifically, to improve the net vision quality obtained by the entire lens-eye optical system by accounting for the optical interaction between the high-order wavefront aberrations of the eye and the high-order aberrations produced by the ophthalmic lens element over the lens aperture.